Group delay measurements using modally selective Lamb wave transducers for detection and

Transcription

1 HOME SEARCH PACS & MSC JOURNALS ABOUT CONTACT US Group delay measurements using modally selective Lamb wave transducers for detection and sizing of delaminations in composites This article has been downloaded from IOPscience. Please scroll down to see the full text article Smart Mater. Struct ( The Table of Contents and more related content is available Download details: IP Address: The article was downloaded on 13/02/2009 at 20:22 Please note that terms and conditions apply.

2 IOP PUBLISHING Smart Mater. Struct. 17 (2008) (9pp) SMART MATERIALS AND STRUCTURES doi: / /17/01/ Group delay measurements using modally selective Lamb wave transducers for detection and sizing of delaminations in composites G Petculescu, S Krishnaswamy and J D Achenbach Center for Quality Engineering and Failure Prevention, Northwestern University, Evanston, IL 60208, USA Received 2 June 2007, in final form 10 October 2007 Published 27 November 2007 Online at stacks.iop.org/sms/17/ Abstract A group delay measurement technique is proposed using modally selective Lamb wave transducers for the detection and sizing of delaminations in unidirectional and cross-ply composites. Unlike amplitude or energy based Lamb wave methods, this method is insensitive to transducer coupling. Specifically, modally selective array transducers are used to generate the lowest antisymmetric A 0 Lamb mode in a zone with minimal dispersion. The change in the modal group velocity is used as a damage indicator while the accumulated time delay of the traveling ultrasonic wavepacket is used for size estimation of the delaminations. The results are repeatable and consistent, suggesting time delay as a reliable damage parameter for quantitative monitoring of delaminations and impact damage in composites. 1. Introduction Ultrasonic techniques, such as C-scans and Lamb wave methods, are well established tools for nondestructive investigation. Lamb waves in particular have proven to be efficient for inspecting plate- and pipe-like components [1 4] as they interrogate the entire thickness of such structures and propagate over extended distances even in composite materials. With a small number of tests, Lamb waves can be used to interrogate large plate-like structures, through the thickness, and in unreachable areas. Experimental and theoretical aspects of Lamb wave propagation in stratified media with direct applications to composites have been addressed since the late 1980s. A selection of early works presented in a special ASME session can be found in [5]. The exploration of guided wave effectiveness to damage detection in composites followed soon after. Examples of early investigations can be found in Rose et al [6] and Guo and Cawley [7]. The particular displacement, stress and strain profiles throughout the thickness of the composite of the various modes relative to the location of the damage was shown to be essential for the sensitivity of detection. Rose et al gave further insight on the general strategy and criteria to be used in guided wave techniques for layered media. Various approaches have been used since for delamination characterization [8]. The resonant method for delamination detection is effective but its sensitivity depends on the proximity of delaminations to the nodes of the normal mode in use [9]. Reflection signals were shown to be an effective method for detecting the presence and location of delaminations [10, 11] but the technique cannot be used to determine the extent of the damage with reasonable precision. Monitoring either the amplitude or the magnitude of the wavelet coefficients of a transmitted ultrasonic signal has also been suggested as a potential way to identify underlying defects [12]. One drawback is that variability in the coupling and the sensitivity of transducers can induce changes in the amplitude and energy of the signal that are often comparable with those caused by damage. In contrast, velocimetric methods [13] which track changes in ultrasonic velocities due to variations in geometry or material properties can be used reliably for damage detection. For instance, the variation of Lamb wave velocities with thickness has been previously used to investigate corrosion damage in metals [14, 15], and to identify delaminated zones in GLARE composites [16]. In the present work, we demonstrate that modally selective array transducers can be effectively used in a velocimetric sense /08/ $ IOP Publishing Ltd Printed in the UK

3 Figure 1. Specimen I, a carbon epoxy plain-weave quasi-isotropic composite panel. to detect and estimate delaminations and impact damage in quasi-isotropic woven and cross-ply composites. The size of delaminations (1.5, 1, 0.75, and 0.5 inch) located in the midplane of a composite panel is calculated with good precision from the measured damage parameter. 2. Methodology Two types of delaminations are investigated. First, artificial mid-plane delaminations simulated through inserts of various types and sizes introduced in a quasi-isotropic woven composite panel during fabrication were analyzed. The material is of interest because of its industrial applications as a versatile composite with improved impact resistance. In a second set of experiments, impact-induced delaminations in a cross-ply composite panel were monitored. The composite plates were subjected to low velocity impact which produces delaminations distributed at multiple interfaces through out the thickness of the panel. Matrix cracking and fiber breaking were also present. For both specimens, the lowest antisymmetric Lamb mode, A 0, excited selectively in a frequency domain with low dispersion is used for detection and sizing of the damaged area. For the specimen with inserts, variations in the modal group velocity along with some wave scattering and possibly mode conversion were observed. For the impacted specimen, the cumulative effect of the complex damage is to lower the modal group velocity, although for this case the effect is produced through a different mechanism. To reiterate, group velocity changes of wavepackets propagating through zones with and without damage are the basis for the quantitative detection method used here. To facilitate an accurate and direct way to monitor velocity changes, array-type modally selective Lamb wave transducers were used to selectively generate and receive the lowest antisymmetric Lamb mode, A 0. The transducers, fabricated in the laboratory using PVDF film, are low cost, very thin and malleable, properties that make them particularly suitable for online structural health monitoring Specimens Specimen I is a carbon epoxy plain-weave quasi-isotropic composite panel manufactured by Cytec Industries, with inserts in the mid-plane (figure 1). The panel has two sections, one with 16 and the other with 24 plies, laid up in a [0/45/-45/90] 2S and [0/45/-45/90] 3S configuration, respectively. The transition between the 3.7 and 5.6 mm of the two sides is gradual, layer by layer. Inserts of different types (2-ply pillow, 4-ply pillow, inch thick Teflon, and inch thick Grafoil) with various diameters (1.5, 1, 0.75, 0.5, 0.25 inch) were introduced in the panel s mid-plane during fabrication. The n-ply pillow insert is a layered structure having n layers of tissue paper sealed in between two layers of in thick Kapton film. The specimen also contains flatbottom holes of different sizes as well as pull-tabs. Specimen II, used for impact, is a carbon epoxy crossply composite panel manufactured at the National Institute for Aviation Research, at Wichita State University. The panel is made of 24 plies, BMS 8-276, laid up in a [0/90] 6S configuration. The total thickness of this panel is 4.6 mm Lamb waves Lamb waves are multi-modal and highly dispersive. As such, special care needs to be taken in order to use Lamb waves for time delay measurements. Specifically, it is essential to launch a single mode at a desired frequency range where the Lamb wave dispersion for that mode is minimal. The Lamb wave dispersion curves for the specimens used in the present experiments were calculated numerically using the classical transfer matrix method for layered media [17, 18] and are shown in figure 2. The surrounding medium is assumed to be vacuum. The SH (shear horizontal) modes that are also obtained as solutions are not included in the figure. The 2

4 Figure 2. Numerically calculated phase velocity dispersion curves (solid and dashed lines are used for asymmetric and symmetric modes, respectively) for Lamb waves in the composite materials investigated, (a) specimen I: woven [0/45/-45/90] 2S, (b) specimen II: cross-ply [0/90] 6S. The propagation direction of the waves is along the 0 angle. Table 1. Material properties of a layer (axis 1 is along the propagation direction) used in calculating the dispersion curves (figure 2) of the specimens used in the experiments. In the calculation, each layer is rotated according to the lay-up scheme. Note the 1 2 and 2 3 symmetry for the first and second specimens, respectively. E 11 (GPa) E 22 (GPa) E 33 (GPa) G 12 (GPa) G 13 ρ (GPa) ν 12 ν 13 ν 23 (kg m 3 ) Specimen I (woven) Specimen II (cross-ply) material properties used in the calculations are given in table 1. For the woven specimen, the E 11 modulus and the density were known from the manufacturer while the other quantities are the typical values found for carbon/epoxy plain-woven prepreg. For the cross-ply specimen, the numbers used are generic values that were obtained from the manufacturer for the type of prepreg used to fabricate the specimen. The A 0 mode was chosen in the current investigation for several reasons: (i) the A 0 mode has an extended domain with low dispersion (at f D > 0.2 MHz mm), (ii) the small wavelength of the A 0 mode (λ mm for the given specimens) provides high resolution of detection, and (iii) the A 0 mode is sensitive to defects located in the midplane. Generally, the S 0 mode can also be used in its low dispersion region at low f D values. The S 0 mode has the additional benefit of lower attenuation but the combination of high velocities and low frequencies produces wavelengths on the order of 40 mm which can have an undesirable effect on the resolution of the measurements Transducers Excitation and detection of individual Lamb modes is possible through various techniques [19 21]. The basic idea is to use an array of sources ( a comb ), with the element spacing dictated by the wavelength of the desired mode and the drive frequency chosen to be in a minimally dispersive region of the Lamb wave dispersion curve. This ensures that the Lamb wavepacket maintains its shape over extended propagation distances. In this work, a matched pair of modally selective transducers is used for generation and reception. This enables time delay measurements to be performed (since any mode converted waves in the defect region will not be seen by the receiving transducer as it is matched to see only the generated mode). Transducers designed for Lamb wave excitation and detection [22] in aluminum plates have been analyzed by Castaings et al [23], Monkhouse et al [24], and Rose et al [25]. Although the electrode structure of the Lamb wave transducers is very similar to that of interdigital surface acoustic wave (SAW) devices, the piezoelectric substrate of the existing Lamb wave transducers is much thinner and it is poled in the thickness direction. We use a simple design with a single set of fingers at the same potential [25] instead of two sets driven at opposite phase as in [23, 24]. This eliminates the need for high voltage RF transformers. The fingers are spaced at a distance λ 0 apart. The piezoelectric material used is 110 µm thick PVDF (polyvinylidene fluoride) [26, 27], which is thin and flexible, producing malleable sensors with a very low profile, low Q, and a minimal cost. These are important attributes for sensors intended to be used in structural health monitoring. The total thickness of the sensor of 0.3 mm (PVDF thin film plus metal electrode) is not tuned to resonate at a specific frequency. The lower piezoelectric constant of PVDF (33 pm V 1 ) versus that of other piezoelectrics (e.g. PZT, 590 pm V 1 ) is partially compensated by a better transmission between the transducer and the composite specimen due to a better acoustic impedance match (Z PVDF = g cm 3 s 1 ) Experimental procedure A matched pair of modally selective array transducers was used in a pitch catch mode to generate and detect the Lamb waves. For the proof-of-concept experiments, the transducers 3

5 Figure 3. Type I scan: transducers are translated in the x direction, waves propagate along the y direction. Measurements were taken when the transducers center line coincides with the center of a defect (1, 3, etc) and also in between defects, at equal distance from two neighboring defects (2, 4, etc). were coupled to the specimen through a layer of honey. The composite panel was grounded at one corner. In real applications, these transducers would be permanently installed using conductive epoxy which provides acoustic coupling and a good ground electrode. A function generator and a gated RF amplifier were used to generate a 10-cycle tone burst with V RMS = 115 V which was used to drive the generating transducer. The signal picked up at the matched receiver was passed through the amplification stage of a Panametrics 5055 pulser receiver and a low pass (LP) 2.5 MHz filter for noise reduction. An impedance based matching network for the receiver or/and the generating transducers to improve the signal-to-noise ratio (S/N) was used in some cases. Since neither one of the transducers was shielded, a large electromagnetic pickup between the source and the receiver is visible in all the signals recorded. However, the Lamb wave signal of interest is well separated in time from the EMI signal. 3. Detection of artificial delaminations 3.1. Modal purity The single-mode propagation characteristics of the A 0 mode were verified for the x and y directions of specimen I (figure 1) on the 3.7 mm thick part of the panel. The transducers (λ 0 = 4.5 mm) were excited at a frequency of f = 0.31 MHz. The mode is observed to be stable, maintaining its group velocity and shape over an extended propagation distance. The group velocity, estimated from the linear fit of distance versus peakarrival data is c x = mm µs 1 (fit correlation coefficient rcx 2 = ). For the y direction, the linear fit yields c y = mm µs 1 (with rcy 2 = ). The values measured for the group velocity correspond to what we expect for the A 0 mode in this material at this thickness and frequency ( f D = MHz mm), based on the theoretical dispersion curve. The attenuation coefficients for the two directions are estimated to be α x = Np cm 1 (fit correlation coefficient rαx 2 = ) and α y = Np cm 1 (with rαy 2 = ) from a linear fit of ln(v pp) versus propagation distance. Overall, the propagation of the mode along x or y has very similar characteristics, as expected for this composite lay-up Results for artificial delaminations Two types of scans were performed for the woven panel (specimen I) using the A 0 mode: type I scans along the x axis, looking at inserts of the same type but different sizes, and type II scans along the y axis, looking at inserts of the same size but different types. The received signals were recorded at specific locations of the transducers. These locations (1, 2, 3,...) are shown in figure 3 for a type I scan. The odd-numbered propagation paths, hereafter called across paths, pass through the center of the defects. The evennumbered propagation paths, hereafter called not-across paths, are equidistant between two neighboring defects probing the undamaged composite. The distance between the edges of neighboring defects on the y axis grows from 38 mm for the row with largest defects (1.5 inch in diameter) to 70 mm for the row with smallest defects (0.25 inch in diameter). For the x axis, the distance between the edges of neighboring defects is fixed to 40 mm for all rows. Great care was taken to maintain a constant distance between the source and the receiver as this was crucial for the accuracy of the measurements. For each scan, two parallel guiding rails, secured to the panel, were used. At each measurement, the transducers were pushed flush against their associated rail and taped to the rail. Checks of parallelism between the two rails were done before and after the scans. No shifts were found. Variations in the source receiver distance coming from accidental gaps between the transducers and their associated rail are estimated to a maximum of 0.5 mm or a time delay of 0.3 µs. Note that, since the rails are on the outside of the monitored area, errors in time delay due to gaps between the transducer and the rail can only underestimate the actual time delay mm thick side, [0/45/-45/90] 2S. Time traces from nine across and not-across paths in a type I scan for the Teflon inserts are shown in figure 4(a). While the signals from the not-across positions consistently arrive at the same time, the signals from the across positions exhibit clear delays, apparently correlated with the size of the defect. The electromagnetic pickup, in phase for all signals, is also visible. The time delay for each across signal (the tone-burst part) was calculated by cross correlating it with a reference signal that corresponds to one of the not-across paths. The results from two separate runs are plotted in figure 4(b), using position 2(x = 9 cm) as reference. The [XC, lags] = xcorr(sig, ref) function of Matlab was used to calculate the cross correlation between the signals and the reference. The time delay is estimated from the array index of the absolute maxima of the vector XC (length 2N + 1 for signals of length N), as lags(max( XC )) dt, where dt is the digitization interval of the time domain. The resolution in the time domain in the correlation calculation is 0.02 µs. Errors up to 0.3 µs are possible due to variability in the source receiver distance, as described in section 3.2. The procedure used to determine the time delay could be any of the standard methods used to determine time of flight. While the necessary precision and accuracy will vary with the application, the chosen method has to be usable in a stand-alone neuronal-network-type algorithm for time delay determination. 4

6 Figure 4. Type I scan of the row of Teflon inserts (from 1.5 to 0.25 inch) on the 3.7 mm side of the panel. (a) Time traces from nine across and not-across paths (full trace in the upper plot and zoom in the lower). (b) The time delay calculated for the nine traces, using position 2 as reference. Two repeated scans are plotted. Figure 5. Type I (a) and type II (b) scans on the 3.7 mm side of the panel. The time delay is calculated for (a) the 4-ply pillow inserts (diameter from 1.5 to 0.25 inch) and (b) different-type inserts of various sizes (1, 0.75, and 0.5 inch) is shown. Two repeated scans are shown in (a). The average of two scans is used for each curve in (b). A similar set of measurements was taken for the row of 4- ply pillow inserts. The calculated time delay values are plotted in figure 5(a). Type II scans were performed for the columns with inserts of size 1 inch, 3/4 inch, and 1/2 inch. The time delay extracted from the time traces is plotted for all three sizes in figure 5(b). Each point is the average of measurements taken during two separate scans. As in the scans of type I, the data had very good reproducibility between the repeated scans mm thick side, [0/45/-45/90] 3S. Measurements were also carried out for the thicker part of the panel (24 ply). One scan of type I was performed for the row with Teflon inserts of different sizes and one scan of type II was performed for the column with 0.75 inch inserts of different types. The time delay data calculated from the two scans are plotted in figures 6(a) and (b), respectively Analysis In regions where the composite panel is undamaged, the wave propagates with minimal dispersion at the chosen f D value at which it is excited. As the wave reaches the area where the insert separates the panel in two symmetric sections with half the original thickness and (ideally) with free surfaces, the wave is forced to propagate through the two adjoining sections with 5

7 Figure 6. Type I (a) and type II (b) scans on the 5.6 mm side of the panel. Time delay is calculated for (a) Teflon inserts (diameter from 1.5 to 0.25 inch) and (b) different type inserts of 0.75 inch diameter is shown. Position 2 (x = 9 cm) and position 1 (x = 4 cm), are used as reference in the correlation calculation, respectively. Two repeated scans are shown in each plot. The location of the inserts is shown below the plot. Figure 7. Geometry used for calculating the time delay at the receiver. The sketch shows the < 2w case only (2w = 20 mm in the experiment). half the original f D. The wave velocity at f D 1/2 is slightly lower, which is the cause of the time delay in the received pulse. Subsequent to the defect region, the wave continues to propagate at the velocity corresponding to the original f D value. Clearly, the time delay will depend on the size and shape of the defect. If a relationship can be established between them, then a quantitative evaluation of the defect can be done. A simple calculation can be carried out based on the geometry shown in figure 7. The transducers span an area which is 2w wide along the x axis (w = 10 mm in the experiment). Now consider a ray indicated by the dashed line in figure 7. The time delay of the signal corresponding to the path along that ray is given by t(x) = d(x) c 1/2 d(x) c, (1) where is the defect diameter, c is the velocity at f D, c 1/2 is the velocity at f D 1/2, and d(x) is the distance traveled across the delamination, d(x) = 2 ( /2) 2 x 2. Averaged over the diameter of the defect (or the width of the active area of the transducers when the defect exceeds that area, i.e. > 2w), the average time delay accumulated by all rays between the generating and the receiving transducers becomes 1 /2 ( 1 d(x) 1 ) dx /2 c 1/2 c = π ( 1 1 ), 2w 4 c 1/2 c 1 w ( 1 t = d(x) 1 ) ( 1 dx = 1 ) 2w w c 1/2 c c 1/2 c ( ) 2 w ( ) 2 ( ) 2w sin 1, 2 w 2 2w. (2) The variation of the signal amplitude due to scattering and beam non-uniformity for x [ /2, /2], as well as diffraction and beam spreading are not considered in this simple calculation. The velocity along the y direction of the panel was measured as c = mm µs 1, at full thickness D (section 3.1). Equation (2) can be used for two purposes. If is known, c 1/2 can be calculated using the measured time delay. Conversely, if c 1/2 is known, can be determined. We will apply equation (2) to determine the size of the various 4-ply pillow defects for which the time delay was measured (section 3.2, figure 5(a)), after an average for c 1/2 is calculated. The values of c 1/2 calculated for the 4-ply pillow defects using the average time delays from the measurements (section 3.2.1) in equation (2) are very close (less than 1%) to their mean value of c 1/2 = mm µs 1. The diameters of all the defects estimated from equation (2) and this mean value of c 1/2 are listed in table 2(a). The above algorithm was also applied to determine the size of the Teflon defects from the measured time delay (figure 4). This time, the values of c 1/2 calculated for the five Teflon defects have a larger spread, with four values under 2% and one value at 5% from the mean value of c 1/2 = mm µs 1. The calculated diameters of the 6

8 Table 2. Defect diameter calculated from the time delay measurements in section 3.2 for the 4-ply pillow defects (a) and for the Teflon defects (b). (a) 4-ply pillow defects, 16 ply Defect diameter (inch) Time delay t (average) (µs) Calculated defect diameter (inch) Per cent difference (%) (b) Teflon defects, 16 ply Defect diameter (inch) Time delay t (average) (µs) Calculated defect diameter (inch) Per cent difference (%) Teflon defects are given in table 2(b). The 0.25 inch defect appears to be an outlier. This is better seen in figure 4(b) where the consistency of the results between different sets of measurements is weakest for the 0.25 inch defect Discussion The results obtained for the 24-ply side of the panel show consistently smaller time delays for a given size and type of defect than those seen for the 16-ply side. This further strengthens the argument used to estimate the diameter of the defects from the velocity at f D 1/2. As the A 0 mode dispersion curve approaches asymptotically its limit at f D, the difference between the velocity c at f D and c 1/2 at f D 1/2 becomes increasingly smaller, which results in a smaller time delay. A more subtle point is raised by the results of the type II scans. Although the defects have the same size, a clear and consistent variation in the time delay is observed between defects of different types. The lowest values are obtained for the Grafoil inserts. We believe the source of for these variations is the surface in the mid-plane, where the insert is located, which is not the ideal free surface considered in the model. The Grafoil insert has the closest acoustic impedance of all to that of the composite material, and it therefore provides the largest deviation from the free surface condition. The 4-ply and the 2-ply inserts, which contain a small amount of trapped air, provide an almost free surface at half-plate, these inserts being the closest imitation of a real delamination. For real defects with unknown locations, the scanning has to be replaced by x y tomography with a number of transducers permanently mounted on the structure. The interpretation of the tomography data based on velocity changes obtained from oblique and normal incidence paths is the subject of future work and it constitutes a step toward verifying the effectiveness of the method for real life applications. 4. Detection of impact damage The results included in this section indicate the effect of natural damage on the quantity time delay, the damage parameter Modal purity The single-mode propagation characteristics of the A 0 mode at f = 0.32 MHz for specimen II were first verified. The group velocity (propagation direction along the fibers of the first layer) was measured to be c = mm µs 1 (fit correlation coefficient rc 2 = ) and the attenuation coefficient α = Np cm 1 (fit correlation coefficient rα 2 = ) Results for impact damage Coupons 1.5 inch by 12 inch were cut from the cross-ply specimen, with the 12 inch side parallel to the fiber direction of the first layer. The matched generation and receiving transducers were fixed at 90 mm distance apart. An impactor with a 1 inch radius steel ball tip was used to produce the damage in the composite area between the transducers. A guiding rail was used to control the location of the impact with an estimated precision of 2 mm. The impact was applied at the same point 30 consecutive times with a constant energy of 22 J. The time traces of the received signal recorded after each impact are displayed in figure 8(a). Plots of the amplitude and time delay of the pulse as a function of the number of impact events were extracted from the time traces and are shown in figure 8(b). The experiment was repeated with the impact energy of 28 J. The time delay and amplitude data are displayed in figure 8(b) as well. For both energy levels, the time delay is shown to grow steadily as the damage accumulates. The rate of increase follows the same trend for both sets of impact. The amplitude, however, evolves in a less clear way as can be seen in figure 8(b). The results further confirm the necessity of utilizing a damage parameter other than the signal amplitude to monitor the existence and amount of damage. The reason that the amplitude follows an unpredictable trend could be due to the opening and closing of delaminated regions with subsequent impact. A C-scan image of the damaged coupon was done after all impacts and is shown in figure Discussion The damage created by impact involves not only delaminations at multiple interfaces, but also matrix and fiber damage. The overall effect is consistent with the lowering of the effective material stiffness, which results in a lower velocity (and therefore an increasing time delay). When the impact is applied at the same spot, the damage accumulates, even though not necessarily linearly. For the two impact loads, the rate of increase of the time delay with the number of impact events appears to have the same trend, with a faster accumulation of damage for the larger impact. An empirical relationship between the measured time delay and the size of the damage can be obtained from a C-scan image showing the size of the damaged area after each of the impact events. Empirical methods to correlate the time delay with the degree of damage are at present the best approach for the quantitative determination of impact damage since the details of the process which leads to a decrease in stiffness, plus other mechanisms which contribute to lowering the wave velocity, are not yet well 7

9 Figure 8. (a) Time traces of the received signal (A 0 mode) in the 22 J impact test, as damage progresses. The top trace corresponds to no damage. Measurements were made after each impact and are shown in sequence. (b) Amplitude and time delay of the A 0 pulse as a function of impact for two impact energies, extracted from the time traces. induced by impact. In this case, it is shown that the time delay damage parameter indicates a more stable, predictable result, when compared with amplitude variation as a damage parameter. Acknowledgments Figure 9. C-scan of the impacted cross-ply coupon in the damaged area at the location of the two hit points (28 and 22 J). understood. If multiple modes are used for inspection (one at a time), it is expected that the damage will affect different modes to different degrees, a fact that can be used to further improve the ability to characterize the damage [28]. 5. Conclusions The salient points of this paper are: (1) A matched pair of modally selective transducers was fabricated and used to generate and receive a toneburst Lamb wave packet. When the wavepacket travels through a damaged region, the group velocity changes which results in a time delay in the received wavepacket. Since the receiving transducer is matched to that of the generating transducer, any mode converted waves due to the defect are not seen by the receiving transducer. (2) Simulated delaminations are detected and their size is correctly estimated based on the measured damage parameter, the time delay. A simple ray analysis taking into account the change in group velocity (induced geometrically by the defect) accurately accounts for the measured time delays. (3) A similar exercise indicates that the proposed time delay damage parameter can also be used for real damage We thank Lamia Salah from the National Institute for Aviation Research for preparing the cross-ply specimen and Kirk Rackow from Sandia National Laboratories for providing the woven composite panel. We thank John Townsley from Boeing Phantom Works for information on material properties of woven composite. We are grateful to Sang-Woo Choi for taking the C-scan image. This work was supported by the Federal Aviation Administration. References [1] Worlton D C 1961 Experimental confirmation of Lamb waves at megacycle frequencies J. Appl. Phys [2] Chimenti D E 1997 Guided waves in plates and their use in materials characterization Appl. Mech. Rev [3] Alleyne D N and Cawley P 1992 The interaction of Lamb waves with defects IEEE Trans. Ultrason. Ferroelectr. Freq. Control [4] Cawley P 1994 The rapid nondestructive inspection of large composite structures Composites [5] Mal A K and Ting T C T (ed) 1988 Wave Propagation in Structural Composites (New York: ASME Press) [6] Rose J L, Pilarski A and Ditri J J 1993 An approach to guided wave mode selection for inspection of laminated plate J. Reinf. Plast. Compos [7] Guo N and Cawley P 1993 The interaction of Lamb waves with delaminations in composite laminates J. Acoust. Soc. Am [8] Giurgiutiu V and Cuc A 2005 Embedded non-destructive evaluation for structural health monitoring, damage detection, and failure prevention Shock Vib. Dig

10 [9] Banks H T, Inman D J, Leo D J and Wang Y 1996 An experimentally validated damage detection theory in smart structures J. Sound Vib [10] Ip K-H and Mai Y-W 2004 Delamination detection in smart composite beams using Lamb waves Smart Mater. Struct [11] Yang M and Qiao P 2005 Modeling and experimental detection of damage in various materials using the pulse-echo method and piezoelectric sensors/actuators Smart Mater. Struct [12] Kessler S S, Spearing S M and Soutis C 2002 Damage detection in composite materials using Lamb wave methods Smart Mater. Struct [13] Cawley P 1990 The detection of delaminations using flexural waves NDT Int [14] Hinders M K and McKeon J C P 1998 Lamb wave tomography for corrosion mapping Proc. 2nd Joint NASA/FAA/DoD Conf. on Aging Aircraft pp [15] Hildebrand B P, Davis T J, Posakony G J and Spanner J C 1999 Lamb wave tomography for imaging erosion/corrosion in piping Rev. Prog. Quant. Nondestruct. Eval [16] Demcenko A, Zukauskas E, Kazys R and Voleisis A 2005 Investigation of interaction of the Lamb wave with delamination type defect in GLARE composite using air-coupled ultrasonic technique Proc. Forum Acusticum (Budapest) pp [17] Nayfeh A H 1995 Wave Propagation in Layered Anisotropic Media with Applications to Composites (Amsterdam: Elsevier) [18] Lowe M J S 1995 Matrix techniques for modeling ultrasonic waves in multilayered media IEEE Trans. Ultrason. Ferroelectr. Freq. Control [19] Viktorov I A 1967 Rayleigh and Lamb Waves: Physical Theory and Applications (New York: Plenum) [20] Nagata Y, Huang J, Krishnaswamy S and Achenbach J D 1994 Lamb wave tomography using laser-based ultrasonics Rev. Prog. Quant. Nondestruct. Eval [21] Guo Z, Achenbach J D and Krishnaswamy S 1997 EMAT generation and laser detection of single Lamb wave modes Ultrasonics [22] Mattiocco F, Dieulesaint E and Royer D 1980 PVF/sub 2/transducers for Rayleigh waves Electron. Lett [23] Castaings M, Monkhouse R S C, Lowe M J S and Cawley P 1999 The performance of flexible interdigital PVDF Lamb wave transducers Acust., Acta Acust [24] Monkhouse R S C, Wilcox P W, Lowe M J S, Dalton R P and Cawley P 2000 The rapid monitoring of structures using interdigital Lamb wave transducers Smart Mater. Struct [25] Rose J L, Pelts S P and Quarry M J 1998 A comb transducer model for guided wave NDE Ultrasonics [26] Gachagan A et al 1999 Generation and reception of ultrasonic guided waves in composite plates using conformable piezoelectric transmitters and optical-fiber IEEE Trans. Ultrason. Ferroelectr. Freq. Control [27] Hay T R and Rose J L 2002 Flexible PVDF comb transducers for excitation of axisymmetric guided waves in pipe Sensors Actuators A [28] Petculescu G, Krishnaswamy S and Achenbach J D 2006 Selective excitation of Lamb-waves for damage detection in composites Rev. Prog. Quant. Nondestruct. Eval